Putting baby down to sleep awake

L
My son is just about 3 months old and as a ftm i didnt know the importance of putting him down drowsy but awake to go to sleep. Now we are having the issue of rocking to sleep, and back to sleep, and back to sleep again as he wakes almost every time we put him down. And then the endless putting the pacifier back in his mouth because he cant do that yet.  Hes also become a terrible catnapper so he is often cranky and tired. 
All the sleep methods Ive read say you cant start until at least 4 months, does anyone have any advice for the meantime to undo the monster we unintentionally created? Is leaving them to fuss and see if they fall back to sleep at this age mean and pointless? Very tired over here, both me and my son!